JEE Math Practice Question

A box open from top is made from a rectangular sheet of dimension a $$\times$$ b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :

1. A.$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over {12}}$$
2. B.$${{a + b - \sqrt {{a^2} + {b^2} + ab} } \over 6}$$
3. C.$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over 6}$$
4. D.$${{a + b + \sqrt {{a^2} + {b^2} + ab} } \over 6}$$